Obviously, it can be done, as dry yeast works for fermenting beer. I go sometimes a month or two between batches, and carrying over one yeast culture across beers seems a bit of a pain. How is dried yeast made/ packaged? Is it something a homebrewer can reasonably do?

I don't think the process of commercially drying yeast is straightforward - it involves a partial vacuum or a stream of filtered air to make the liquid suspending the yeast evaporate faster - and it's probably difficult to reach the levels of hygiene required in a homebrew setting.

If you want to preserve yeast for a long period, 1 year or more, you can store the yeast with glycerine and keep it in the freezer. There's a good writeup on HBT with the process and equipment needed. It's fairly simple and achieves good results. I've successfully brewed with yeast that I froze 3 years ago.

Even if you don't freeze the yeast, but keep the yeast in the fridge, the yeast remain in better condition in glycerine than when kept in wort.

If you are already making a starter then freezing is a simple process that allows you to keep a variety of strains in your yeast bank over a long period.